Recently, there has been growing demand for multimedia computing and communication. This growing demand has motivated searches for better bandwidth management techniques, including newer and more efficient compression methods.
Today's mainstream compression methods, such as JPEG for still images and MPEG for video, use the Discrete Cosine Transform (DCT). The sinusoidal basis functions of the DCT have infinite support and so each sinusoidal basis function provides perfect frequency resolution but no spatial resolution. At the other extreme, impulse basis functions have infinitesimal support, so each impulse basis function provides perfect spatial resolution but no frequency resolution. However, neither sinusoidal nor impulse basis functions are very well suited for the purposes of image and video compression. Better suited are basis functions which can trade-off between frequency and spatial resolution.
The wavelet basis functions of a wavelet transform are such basis functions in that each wavelet basis function has finite support of a different width. The wider wavelets examine larger regions of the signal and resolve low frequency details accurately, while the narrower wavelets examine a small region of the signal and resolve spatial details accurately. Wavelet-based compression has the potential for better compression ratios and less complexity than sinusoidal-based compression. The potential for wavelet-based compression is illustrated by FIGS. 19, 20, and 21. FIG. 19 is an original 8 bits per pixel 512.times.512 image of "Lena." FIG. 20 is a reconstructed image of Lena after JPEG compression at a compression ratio of approximately 40. FIG. 21 is a reconstructed image of Lena after wavelet compression at a compression ratio of approximately 40 using a preferred embodiment of the present invention. FIG. 21 appears less "blocky" than FIG. 20 because of the varying widths of the wavelet basis functions.
For a practical discussion of wavelet-based compression, see, for example, "Compressing Still and Moving Images with Wavelets," by Michael, L. Hilton, Bjorn D. Jawerth, and Ayan Sengupta, in Multimedia Systems, volume 2, number 3 (1994). Another useful article is "Vector Quantization," by Robert M. Gray, in IEEE ASSP Magazine, April 1984. Both the above articles are herein incorporated by reference in their entirety.
Prior systems and methods for inverse wavelet filtering use conventional filters. A conventional filter does not efficiently compute the inverse wavelet transform of an image because it does not take advantage of the fact that its input is an upsampled stream of data.